Compute UVP diversity metrics

Compute taxonomic, morphologic and trophic diversity metrics from UVP5 plankton data.

source("utils.R")

Read UVP data

load("data/00.all_uvp.Rdata")

Clean data

Depth

Keep only organisms above the depth at which we want to predict poc export, i.e. 1000 m.

o <- o %>% filter(between(depth, min_depth_uvp, max_depth_uvp))
#o <- o %>% filter(between(depth, 0, max_depth_uvp))

Taxa

List taxa, merge contextual observations with regular observations. Remove some unwanted taxa: tentacles of Cnidaria (only part of organisms, not representative of the overall morphology), Trichodesmium, Nostocales and Bacillariophyta (phytoplankton).

# List of taxa
taxa <- o %>% pull(taxon) %>% unique() %>% sort()
taxa

 [1] "Acantharea"                   "Actinopterygii"              
 [3] "Annelida"                     "Appendicularia"              
 [5] "Bacillariophyta (contextual)" "Cephalopoda"                 
 [7] "Chaetognatha"                 "colonial Collodaria"         
 [9] "Copepoda"                     "Ctenophora"                  
[11] "Doliolida"                    "Eumalacostraca"              
[13] "Foraminifera"                 "Gymnosomata"                 
[15] "Limacinidae"                  "Narcomedusae"                
[17] "Nostocales"                   "Ostracoda"                   
[19] "other Cnidaria"               "other Collodaria"            
[21] "other Crustacea"              "other Hydrozoa"              
[23] "other Mollusca"               "other Rhizaria"              
[25] "Phaeodaria"                   "Pyrosoma"                    
[27] "Salpida"                      "Siphonophorae"               
[29] "tentacle of Cnidaria"         "Thecosomata"                 
[31] "Trachymedusae"                "Trichodesmium"               
[33] "Trichodesmium (contextual)"  

# Merge contextual
o <- o %>% mutate(taxon = str_remove_all(taxon, " \\(contextual\\)")) # NB need to use \\

# List unwanted taxa
unwanted <- c("Bacillariophyta", "Nostocales", "tentacle of Cnidaria", "Trichodesmium")
o <- o %>% filter(!taxon %in% unwanted)

# New list of taxa
taxa <- o %>% pull(taxon) %>% unique() %>% sort()
taxa

 [1] "Acantharea"          "Actinopterygii"      "Annelida"           
 [4] "Appendicularia"      "Cephalopoda"         "Chaetognatha"       
 [7] "colonial Collodaria" "Copepoda"            "Ctenophora"         
[10] "Doliolida"           "Eumalacostraca"      "Foraminifera"       
[13] "Gymnosomata"         "Limacinidae"         "Narcomedusae"       
[16] "Ostracoda"           "other Cnidaria"      "other Collodaria"   
[19] "other Crustacea"     "other Hydrozoa"      "other Mollusca"     
[22] "other Rhizaria"      "Phaeodaria"          "Pyrosoma"           
[25] "Salpida"             "Siphonophorae"       "Thecosomata"        
[28] "Trachymedusae"      

Profiles

Compute the number of objects per profile and keep only profiles that have more than 10 objects.

profiles <- o %>% 
  group_by(profile_id, lon, lat, datetime) %>% 
  summarise(n_obj = n()) %>% 
  ungroup()

profiles %>% 
  ggplot() +
  geom_histogram(aes(x = n_obj), bins = 50) +
  scale_x_continuous(limits = c(0, 50)) #+

  #scale_y_continuous(trans = "log1p")
  #scale_y_log10()

profiles %>%
  ggplot() +
  geom_polygon(data = world, aes(x = lon, y = lat, group = group), fill = "gray") +
  geom_point(aes(x = lon, y = lat, colour = n_obj > n_min_uvp), size = 0.5) +
  scale_x_continuous(expand = c(0, 0)) + scale_y_continuous(expand = c(0, 0)) +
  coord_quickmap()

# Keep only profiles with enough objects
profiles <- profiles %>% filter(n_obj > n_min_uvp) %>% select(-n_obj)

# Drop objects that do not belong to these profiles
o <- o %>% filter(profile_id %in% profiles$profile_id)

We have 187707 objects belonging to 2366 profiles.

Proportions of large taxonomic groups

Compute proportions of large taxonomic groups.

props <- o %>% 
  select(lon, lat, profile_id, taxon, large_group) %>% 
  count(lon, lat, profile_id, large_group) %>% 
  group_by(lon, lat, profile_id) %>% 
  mutate(prop = n/sum(n)) %>% 
  ungroup() %>% 
  select(lon, lat, profile_id, large_group, prop) 

# Plot a map
ggplot(props) + 
  geom_polygon(data = world, aes(x = lon, y = lat, group = group), fill = "grey") +
  geom_point(aes(x = lon, y = lat, colour = prop), size = 0.5) +
  scale_colour_viridis_c() +
  coord_quickmap(expand = 0) +
  facet_wrap(~large_group, ncol = 2)

# Reformat
props <- props %>% 
  mutate(large_group = paste0("prop_", str_to_lower(large_group))) %>% 
  pivot_wider(names_from = "large_group", values_from = "prop", values_fill = 0)

# Add to profile table
profiles <- profiles %>% 
  left_join(props, by = join_by(profile_id, lon, lat))

Abundance and biovolume

Compute overall abundance and biovolume for each profiles.

# For abundance, just count objects per profile
profiles <- profiles %>% 
  left_join(o %>% count(profile_id, name = "abund"), by = join_by(profile_id))

# For biovolume, compute biovolume for each object and sum per profile
biov <- o %>% 
  select(object_id:taxon, esd) %>% 
  mutate(biovol = (4/3) * pi * esd^3) %>% 
  group_by(profile_id) %>% 
  summarise(biovol = sum(biovol))
# add to profiles
profiles <- profiles %>% left_join(biov, by = join_by(profile_id))

## Plot maps
ggmap(profiles, var = "abund", type = "point", palette = scale_colour_viridis_c(trans = "log1p")) 

ggmap(profiles, var = "biovol", type = "point", palette = scale_colour_viridis_c(trans = "log1p")) 

Taxonomic diversity

Tabula package for diversity indices: https://cran.r-project.org/web/packages/tabula/vignettes/diversity.html

Species richness

• number of species = Richness

• Margalef’s

• Menhinick’s

Diversity / evenness indices

• Shannon

• Brillouin

• Simpson

# Generate a contingency table as a matrix to compute indices
cont <- o %>%
  count(profile_id, taxon) %>%
  pivot_wider(names_from = "taxon", values_from = "n", values_fill = 0) %>%
  as.data.frame() %>%
  column_to_rownames(var = "profile_id") %>%
  as.matrix()

# test for profile id 100
# 65 objects
# 7 taxa
# (7-1)/log(65) # Margalef
# 7/sqrt(65) # Menhinick
# all godd

# Compute diversity metrics
ta_div_prof <- tibble(
  profile_id = rownames(cont),
  # Richess
  ta_ric_1 = specnumber(cont), # species count
  ta_ric_2 = (specnumber(cont) - 1)/log(rowSums(cont)), # Margalef
  ta_ric_3 = specnumber(cont)/sqrt(rowSums(cont)), # Menhinick
  # Heterogeneity/evenness
  ta_div_1 = heterogeneity(cont, method = "shannon"),
  ta_eve_1 = evenness(cont, method = "shannon"),
  ta_div_2 = heterogeneity(cont, method = "brillouin"),
  ta_eve_2 = evenness(cont, method = "brillouin"),
  ta_div_3 = heterogeneity(cont, method = "simpson"),
  ta_eve_3 = evenness(cont, method = "simpson"),
  # Master predictor
  ta_mast = specnumber(cont)/rowSums(cont)
) %>%
  left_join(profiles %>% select(profile_id, lon, lat), by = join_by(profile_id)) %>%
  select(profile_id, lon, lat, contains("ta_"))

# Quick PCA to see correlations
ta_pca <- FactoMineR::PCA(ta_div_prof %>% select(-c(profile_id, lon, lat)), graph = FALSE)
plot(ta_pca, choix = "var")

# ta_eve_1 and ta_eve_2 are strongly correlated, ignore one
ta_div_prof <- ta_div_prof %>% select(-ta_eve_2)

# Store results with table of profiles
profiles <- profiles %>% left_join(ta_div_prof, by = join_by(profile_id, lon, lat))

# ta_eve_1 could not be computed for 9 profiles
# replace by mean value
profiles <- profiles %>% mutate_all(~ifelse(is.na(.x), mean(.x, na.rm = TRUE), .x))  

Plot taxonomic diversity metrics.

ggmap(
  profiles, 
  "ta_ric_1", 
  type = "point"
  )

ggmap(
  profiles, 
  "ta_div_1", 
  type = "point"
  )

ggmap(
  profiles, 
  "ta_eve_1", 
  type = "point"
  )

Size spectra

Compute SS

Compute ss for each profiles.

# Compute SS
# Also compute mean ESD per profile and retain it
ss <- o %>%
  arrange(profile_id) %>%
  group_by(profile_id) %>%
  mutate(mean_esd = mean(esd)) %>%
  ungroup() %>%
  group_by(profile_id, mean_esd) %>%
  reframe(nbss(esd, type = "abundance", base = 10, binwidth = 0.1))

# Plot a few SS, in a log-transformed space
sam_profiles <- profiles %>% slice_sample(n = 12) %>% pull(profile_id)
ss %>% 
  filter(profile_id %in% sam_profiles) %>% 
  ggplot() +
  geom_point(aes(x = bin, y = norm_y)) +
  scale_x_log10() +
  scale_y_log10() +
  facet_wrap(~profile_id)

Clean SS

We need to remove the part left of the peak and keep only profiles that have at least 5 points to fit the SS.

# Use a cumulative sum to remove the part left of the peak
ss <- ss %>%
  group_by(profile_id, mean_esd) %>%
  # Cut the left part of the SS
  filter(cumsum(norm_y == max(norm_y)) > 0) %>%
  ungroup()

# Keep only profiles with at least 5 points to fit SS
ss <- ss %>% add_count(profile_id) %>% filter(n >= 5)

Fit SS

## Fit size spectra
# Log-transform the y value
# NB: not necessary to log-transform x value because already present in the data
ss <- ss %>% mutate(norm_y = log10(norm_y))

# Fit lm
ss_regs <- ss %>% 
  select(profile_id, bin_log, norm_y) %>%
  nest(data = c(bin_log, norm_y)) %>%
  mutate(
    fit = map(data, ~lm(norm_y ~ bin_log, data = .x)), # run lm's
    glance = map(fit, glance),                         # summary of fit
    tidied = map(fit, tidy)                            # extract coefficients
  )


# glance contains all summary of fits
ss_summ <- ss_regs %>%   
  select(profile_id, glance) %>%
  unnest(glance)
summary(ss_summ)

  profile_id          r.squared      adj.r.squared          sigma        
 Length:2003        Min.   :0.2248   Min.   :-0.03365   Min.   :0.04007  
 Class :character   1st Qu.:0.8521   1st Qu.: 0.81879   1st Qu.:0.16751  
 Mode  :character   Median :0.9141   Median : 0.89735   Median :0.21328  
                    Mean   :0.8815   Mean   : 0.85472   Mean   :0.22561  
                    3rd Qu.:0.9515   3rd Qu.: 0.94090   3rd Qu.:0.27441  
                    Max.   :0.9977   Max.   : 0.99711   Max.   :0.79425  
   statistic            p.value                df        logLik        
 Min.   :   0.8698   Min.   :0.0000000   Min.   :1   Min.   :-11.2400  
 1st Qu.:  26.4065   1st Qu.:0.0000746   1st Qu.:1   1st Qu.:  0.2995  
 Median :  54.2815   Median :0.0009053   Median :1   Median :  2.0714  
 Mean   :  85.7861   Mean   :0.0110222   Mean   :1   Mean   :  2.1352  
 3rd Qu.: 102.1958   3rd Qu.:0.0064067   3rd Qu.:1   3rd Qu.:  3.7929  
 Max.   :1724.7354   Max.   :0.4198089   Max.   :1   Max.   : 12.6832  
      AIC               BIC             deviance        df.residual    
 Min.   :-19.366   Min.   :-18.635   Min.   :0.00625   Min.   : 3.000  
 1st Qu.: -1.586   1st Qu.: -1.809   1st Qu.:0.12844   1st Qu.: 4.000  
 Median :  1.857   Median :  1.566   Median :0.23347   Median : 5.000  
 Mean   :  1.730   Mean   :  1.546   Mean   :0.30125   Mean   : 5.125  
 3rd Qu.:  5.401   3rd Qu.:  5.283   3rd Qu.:0.39556   3rd Qu.: 6.000  
 Max.   : 28.480   Max.   : 29.674   Max.   :4.97117   Max.   :13.000  
      nobs       
 Min.   : 5.000  
 1st Qu.: 6.000  
 Median : 7.000  
 Mean   : 7.125  
 3rd Qu.: 8.000  
 Max.   :15.000  

# tidied contains coefficients
ss_coef <- ss_regs %>%
  select(profile_id, tidied) %>%
  unnest(tidied) %>%
  # keep only estimates of slope and intercept
  select(-c(std.error, statistic, p.value)) %>%
  mutate(term = ifelse(term == "bin_log", "b1", "b0")) %>%
  # 2 lines (intercept + slope) for each profile, reshape to make it one line
  pivot_wider(names_from = term, values_from = estimate) #%>% 
  # b0 is intercept, b1 is slope
  #select(profile_id, b1, b0)
summary(ss_coef)

  profile_id              b0               b1         
 Length:2003        Min.   :0.6368   Min.   :-6.4298  
 Class :character   1st Qu.:1.3149   1st Qu.:-3.0929  
 Mode  :character   Median :1.5388   Median :-2.5423  
                    Mean   :1.5859   Mean   :-2.6339  
                    3rd Qu.:1.8038   3rd Qu.:-2.0349  
                    Max.   :3.9929   Max.   :-0.4444  

# Let’s join both together
ss_coef <- ss_coef %>% left_join(ss_summ, by = join_by(profile_id))

# Plot a few fits
ss %>% 
  filter(profile_id %in% sam_profiles) %>% 
  ggplot() +
  geom_point(aes(x = bin_log, y = norm_y)) +
  geom_abline(
    data = ss_coef %>% filter(profile_id %in% sam_profiles), 
    aes(slope = b1, intercept = b0, colour = adj.r.squared)
  ) +
  labs(x = "bin (log)", y = "norm_y (log)", colour = "adj R²") +
  scale_colour_viridis_c() +
  facet_wrap(~profile_id)

Save SS

Join ss outputs with profile data. For profiles for which SS could not be computed (not enough points), replace slope and intercept by the mean value.

profiles <- profiles %>% 
  # join slope and intercept data
  left_join(ss_coef %>% select(profile_id, ss_slope = b1, ss_inter = b0), by = join_by(profile_id)) %>% 
  # replace by the mean value for missing profiles
  mutate_all(~ifelse(is.na(.x), mean(.x, na.rm = TRUE), .x))  

Morphological diversity

Based on:

• https://github.com/jiho/ptb_morphodiv/tree/master

• Magneville et al. 2021

• Beck et al. 2023

• mFD R package

Features

Some features are not meaningful for the morphology and thus should be removed. Other features have a unique value for all individuals and other are missing for many individuals. Let’s remove them.

# Select features
# NB this excludes ratio of features, e.g. kurt_mean which is kurt/mean
x <- o %>% select(area:circex)

# Remove variables with zero variance
feats <- x %>%
  summarise_all(var, na.rm = TRUE) %>%
  pivot_longer(cols = everything()) %>%
  filter(value > 0) %>%
  pull(name)
x <- x %>% select(all_of(feats))

Plot features distributions.

x %>%
  pivot_longer(cols = everything()) %>%
  ggplot() +
  geom_histogram(aes(x = value), bins = 50) +
  facet_wrap(~name, scales = "free")

For a PCA, features should be normally-distributed. Let’s apply some transformation to get closer to normal distribution:

• mask extreme values

• normalize using the Yeo-Johnson transformation

• replace missing values by the mean of each column

x_norm <- x %>%
  # remove the most extreme high values
  mutate_all(mask_extreme, percent = c(0, 0.5)) %>%
  # normalise using the Yeo-Johnson transformation
  mutate_all(yeo_johnson) %>%
  mutate_all(as.numeric)

# Replace NA by average of each column
for (col in names(x_norm)) {
  x_norm[[col]][is.na(x_norm[[col]])] <- mean(x_norm[[col]], na.rm=TRUE)
}

Plot “normalized” features.

x_norm %>%
  pivot_longer(cols = everything()) %>%
  ggplot() +
  geom_histogram(aes(x = value), bins = 50) +
  facet_wrap(~name, scales = "free")

Morphospace

Build

Let’s feed the features to a PCA to build a morphospace.

# We need to use "scale.unit = TRUE" to center-scale all feature
mo_space <- FactoMineR::PCA(x_norm, scale.unit = TRUE, graph = FALSE)

Eigenvalues

Plot the eigenvalues.

eig <- mo_space$eig %>%
  as.data.frame() %>%
  rownames_to_column(var = "comp") %>%
  as_tibble() %>%
  mutate(
    comp = str_remove(comp, "comp "),
    comp = as.numeric(comp),
    comp = as.factor(comp)
    ) %>% 
  rename(var = `percentage of variance`, cum_var = `cumulative percentage of variance`)

eig %>%
  ggplot() +
  geom_col(aes(x = comp, y = eigenvalue)) +
  geom_hline(yintercept = 1, col = "red", linewidth = 0.5) +
  theme_classic() +
  scale_y_continuous(expand = c(0, 0)) +
  labs(x = "PC", y = "Eigenvalue") +
  theme(axis.text.x = element_text(angle = 90, vjust = 0.5, hjust=1))

Most of the variance is captured by the first three axes (0.32, 0.2 and 0.096respectively).

Let’s plot this in log to have a better idea of PCs to select.

eig %>%
  ggplot() +
  geom_path(aes(x = as.numeric(comp), y = eigenvalue)) +
  geom_point(aes(x = as.numeric(comp), y = eigenvalue)) +
  geom_vline(xintercept = 4, colour = "red") +
  theme_classic() +
  scale_x_log10() +
  scale_y_log10() +
  labs(x = "PC", y = "Eigenvalue") +
  theme(axis.text.x = element_text(angle = 90, vjust = 0.5, hjust=1))

It’s linear until ~5, let’s keep the first 5 PCs.

Features and axis definition

Let’s now plot the first two axes.

plot(mo_space, choix="var", axes = c(1, 2))

• PC1: big objects in positive values, small objects in negative values.

• PC2: clear (i.e. transparent) objects in positive values, dark (i.e. opaque) objects in negative values

As well as axes 3 and 4.

plot(mo_space, choix="var", axes = c(3, 4))

• PC3: elongated objects in positive values, round objects in negative values
• PC4: something with grey levels

Individuals

Let’s extract the coordinates of individuals in the morphospace.

## Get coordinates of individuals
inds <- mo_space$ind$coord %>% as_tibble() %>% select(-Dim.5)
# Set nice names for columns
colnames(inds) <- str_c("mo_dim", paste(c(1:ncol(inds))))
# And join with initial dataframe of objects
o <- o %>%
  bind_cols(inds)

We can not plot the position of objects in the morphospace, coloured per profile.

## Plot invidivuals with profile as colour
o %>%
  ggplot(aes(x = mo_dim1, y = mo_dim2, colour = profile_id)) +
  geom_point(show.legend = FALSE, size = 0.5, alpha = 0.05)

Tiling

Let’s now tile morphs within the morphological space.

# Folder containing images
img_dir <- "~/Documents/Data/UVP5/images/"

# Number of features to select
n_feat <- 12

# Generate path to image
o <- o %>% mutate(path_to_img = str_c(img_dir, profile_id, "/", object_id, ".jpg"), .before = object_id) 

# Prepare a circle for the plot
circ <- circleFun(c(0, 0), 2, npoints = 500)


# Get variables contributions
#to select vars based on contribution to each plane
contribs <- as.data.frame(mo_space$var$contrib) %>% as.data.frame()
colnames(contribs) <- str_c("mo_dim", paste(c(1:ncol(contribs))))
contribs <- contribs %>% 
  rownames_to_column(var = "feature") %>% 
  as_tibble() %>% 
  mutate(
    mo_dim_12 = abs(mo_dim1) + abs(mo_dim2),
    mo_dim_23 = abs(mo_dim2) + abs(mo_dim3),
    mo_dim_34 = abs(mo_dim3) + abs(mo_dim4)
  )


# List variables with higher contribution for plane 1:2
var_contrib_12 <- contribs %>% 
  arrange(desc(mo_dim_12)) %>% 
  slice(1:n_feat) %>% 
  pull(feature)

# and for plane 3:4
var_contrib_34 <- contribs %>% 
  arrange(desc(mo_dim_34)) %>% 
  slice(1:n_feat) %>% 
  pull(feature)

# Get types of features
feat_types <- read_csv("data/raw/features_qual.csv", show_col_types = FALSE)
# Set colour per type of feature, using a named vector
feat_colours <- brewer_colors(length(unique(feat_types$type)), "Set2") # pick the appropriate number of colours
names(feat_colours) <- sort(unique(feat_types$type)) # add names to colours

#homogenize scaling between individuals & variables for correct biplot
# Change scaling of variables/columns from scaling 1 to 2
var_scores <- as.data.frame(t(t(mo_space$var$coord) / sqrt(mo_space$eig[,1]))) # de-scale
var_scores_2 <- as.data.frame(t(t(var_scores) * sqrt(nrow(var_scores) * mo_space$eig[,1]))) # re-scale
# Rename columns
colnames(var_scores_2) <- str_c("mo_dim", paste(c(1:ncol(var_scores_2))))
# Add feature names 
var_scores_2 <- var_scores_2 %>% 
  rownames_to_column(var = "feature") %>% 
  as_tibble() %>% 
  # and types
  left_join(feat_types, by = join_by(feature))

# Compute length of projection to scale circle
var_scores_2 <- var_scores_2 %>% 
  mutate(
    len_12 = sqrt(mo_dim1^2 + mo_dim2^2),
    len_34 = sqrt(mo_dim3^2 + mo_dim4^2),
  )

Objects in morphospace for axes 1:2

k <- max(var_scores_2$len_12) # adapt scaling of circle to fit the arrows
p12 <- ggmorph_tile(mo_space, o$path_to_img, steps = 10, n_imgs = 3, fun = preprocess, dimensions = c(1,2), scale = 0.02) 
p12 + 
  geom_path(data = circ, aes(x = x*k, y = y*k), lty = 2, color = "grey", alpha = 0.7) + 
  geom_hline(yintercept = 0, color="grey", alpha = 0.9) +
  geom_vline(xintercept = 0, color="grey", alpha = 0.9) +
  geom_segment(data = var_scores_2 %>% filter(feature %in% var_contrib_12), aes(x = 0, xend = mo_dim1, y = 0, yend = mo_dim2, colour = type), arrow = arrow(length = unit(0.025, "npc"), type = "open")) +
  geom_text_repel(data = var_scores_2 %>% filter(feature %in% var_contrib_12), aes(x = mo_dim1, y = mo_dim2, label = feature, colour = type), show.legend = FALSE) +
  scale_colour_manual(values = feat_colours) +
  labs(colour = "Feature\ntype")

• PC1 = size

• PC2 = transparency

Objects in morphospace for axes 2:3

k <- max(var_scores_2$len_34) # adapt scaling of circle to fit the arrows
p34 <- ggmorph_tile(mo_space, o$path_to_img, steps = 10, n_imgs = 3, fun = preprocess, dimensions = c(3,4), scale = 0.02) 
p34 + 
  geom_path(data = circ, aes(x = x*k, y = y*k), lty = 2, color = "grey", alpha = 0.7) + 
  geom_hline(yintercept = 0, color="grey", alpha = 0.9) +
  geom_vline(xintercept = 0, color="grey", alpha = 0.9) +
  geom_segment(data = var_scores_2 %>% filter(feature %in% var_contrib_34), aes(x = 0, xend = mo_dim3, y = 0, yend = mo_dim4, colour = type), arrow = arrow(length = unit(0.025, "npc"), type = "open")) +
  geom_text_repel(data = var_scores_2 %>% filter(feature %in% var_contrib_34), aes(x = mo_dim3, y = mo_dim4, label = feature, colour = type), show.legend = FALSE) +
  scale_colour_manual(values = feat_colours) +
  labs(colour = "Feature\ntype")

• PC3 = elongation

• PC4 = heterogeneity of grey levels

Diversity

Morphospace features

We can collect the position of objects in the morphospace to summarise the morphological diversity of each profile.

# Compute mean and sd of dim1, dim2, dim3 and dim4 per profile
mo_div_prof <- o %>% 
  group_by(profile_id, lon, lat) %>% 
  summarise(across(mo_dim1:mo_dim4, list(mean = mean, sd = sd))) %>% 
  ungroup()

# And store this with profiles data
profiles <- profiles %>% left_join(mo_div_prof, by = join_by(profile_id, lon, lat))

And we can plot maps of mean dim1 and dim2 values for each profile.

ggmap(
  profiles, 
  "mo_dim1_mean", 
  type = "point", 
  palette = div_pal
  ) +
  labs(colour = "PC1\nSize")

ggmap(
  profiles, 
  "mo_dim2_mean", 
  type = "point", 
  palette = div_pal
  ) +
  labs(colour = "PC2\nTransparency")

ggmap(
  profiles, 
  "mo_dim3_mean", 
  type = "point", 
  palette = div_pal
  ) +
  labs(colour = "PC3\nElongation")

ggmap(
  profiles, 
  "mo_dim4_mean", 
  type = "point", 
  palette = div_pal
  ) +
  labs(colour = "PC4\nGrey hetero.")

We can also look at variance within profiles.

ggmap(
  profiles, 
  "mo_dim1_sd", 
  type = "point"
  ) +
  labs(colour = "PC1 sd\nSize")

ggmap(
  profiles, 
  "mo_dim2_sd", 
  type = "point"
  ) +
  labs(colour = "PC2 sd\nTransparency")

ggmap(
  profiles, 
  "mo_dim3_sd", 
  type = "point"
  ) +
  labs(colour = "PC3 sd\nElongation")

ggmap(
  profiles, 
  "mo_dim4_sd", 
  type = "point"
  ) +
  labs(colour = "PC4 sd\nGrey hetero.")

Metrics

Multivariate morphological diversity metrics have been defined in Beck et al. 2023 following the definition of multivariate functional diversity metrics in Villeger et al. 2008:

• morphological richness

• morphological evenness

• morphological divergence

Actually there is now a R package to compute these metrics. See Magneville et al. 2021 as well as mFD package. Yay!

Computing these metrics require defining “morphs” (i.e. morphologically similar organisms) in the morphospace, i.e. using kmeans. These morphs are then used instead of species to compute morphological diversity metrics.

Define morphs

Define morphs using kmeans, in parallel.

If we retain n morphospace axes, then we need at least n+1 morphs to be present in each profile (to compute a convex hull in n dimensions, we need n+1 points).

# Number of clusters
n_clust <- 200

# Perform clustering
morphs <- wkmeans::wkmeans(
  x = o %>% select(contains("dim")), # use PCA outputs
  k = n_clust, # number of clusters
  nstart = 50, # number of random initialisations, higher is better
  cores = n_cores
  )

# Add cluster to table of objects
o <- o %>% mutate(
  morph = morphs$cluster,
  morph = str_pad(morph, width = nchar(n_clust), pad = "0"), # add leading zeros
  morph = paste0("morph_", morph), # Add "morph_" in front
  morph = as.factor(morph) # convert to factor
)

Look at size of generated morphs (the red vertical line shows the expected mean).

morphs_size <- morphs$size %>% 
  as.data.frame() %>% 
  as_tibble() %>% 
  rename(morph = Var1, n = Freq)

summary(morphs_size)

     morph           n         
 1      :  1   Min.   : 388.0  
 2      :  1   1st Qu.: 705.5  
 3      :  1   Median : 883.0  
 4      :  1   Mean   : 938.5  
 5      :  1   3rd Qu.:1117.5  
 6      :  1   Max.   :2163.0  
 (Other):194                   

morphs_size %>% 
  ggplot() +
  geom_histogram(aes(x = n), bins = n_clust/2) +
  geom_vline(xintercept = nrow(o)/n_clust, colour = "red")

Relation between morph, taxa and profiles.

Number of individuals of each taxon per morph.

# Counts per morph and per taxa
counts_mo_t <- o %>% select(morph, taxon) %>% count(morph, taxon)

counts_mo_t %>% 
  ggplot() +
  geom_boxplot(aes(x = taxon, y = n)) +
  theme(axis.text.x = element_text(angle = 90, vjust = 0.5, hjust=1)) +
  labs(y = "Number per morph") +
  scale_y_continuous(trans = "log1p")

Look at number of taxa per morph.

# Counts per morph
counts_mo <- counts_mo_t %>% count(morph)
ggplot(counts_mo) +
  geom_histogram(aes(x = n, fill = morph), binwidth = 1, show.legend = FALSE) +
  labs(x = "Number of taxa per morph") +
  theme_classic()

# Each colour bloc represents a morph

counts_mo %>% summary()

       morph           n        
 morph_001:  1   Min.   : 5.00  
 morph_002:  1   1st Qu.:12.00  
 morph_003:  1   Median :15.00  
 morph_004:  1   Mean   :15.13  
 morph_005:  1   3rd Qu.:18.00  
 morph_006:  1   Max.   :27.00  
 (Other)  :194                  

The median of number of taxa per morph is 15: morphs are not representative of taxa.

In how many morphs is a taxa present?

# Counts per taxa
counts_t <- counts_mo_t %>% count(taxon)
ggplot(counts_t) +
  geom_col(aes(x = taxon, y = n)) +
  labs(y = "Number of morphs in which taxon is present") +
  coord_flip()

counts_t %>% summary()

    taxon                 n         
 Length:28          Min.   : 21.00  
 Class :character   1st Qu.: 64.75  
 Mode  :character   Median :111.00  
                    Mean   :108.11  
                    3rd Qu.:148.50  
                    Max.   :193.00  

Gymnosomata and Cephalopoda are present in less than 50 morphs, while Copepoda are present in all of them.

Number of morphs per profile. This limits the number of dimensions we can use to compute metrics. We need at least n+1 morphs per profile with n the number of dimensions.

count_p_m <- o %>% count(profile_id, morph)
count_p <- count_p_m %>% count(profile_id) %>% arrange(n)

count_p %>% 
  ggplot() +
  geom_histogram(aes(x = n, fill = n >= 5 ), bins = 50) +
  geom_vline(xintercept = 5, colour = "red")

The red line shows the minimum number of morphs that must be present in each profile in order to compute morphological diversity metrics using 4 morphospace axes.

Plot clusters

o %>%
  ggplot(aes(x = mo_dim1, y = mo_dim2, colour = morph)) +
  geom_point(show.legend = FALSE, size = 0.5, alpha = 0.05)

Compute metrics

We need the following matrices:

• traits values for each morph centre (morphs × traits)

• morphs assemblages (profiles × morphs)

The following metrics are computed (see Magneville et al. 2022):

• fric (functional richness): The volume of the convex hull shaping the species present in the assemblage
• fide (functional identity): The weighted average position of species of the assemblage along each axis. NB: note computed as we already have individuals projections on PCA axes.
• fdis (functional dispersion): The weighted deviation to center of gravity (i.e. defined by the FIde values) of species in the assemblage
• fdiv (functional divergence): The deviation of biomass-density to the center of gravity of the vertices shaping the convex hull of the studied assemblage
• feve (functional evenness): The regularity of biomass-density distribution along the minimum spanning tree (i.e. the tree linking all species of the assemblage with the lowest cumulative branch length) for the studied assemblage
• fori (functional originality): The weighted mean distance to the nearest species from the global species pool
• fspe (functional specialisation): The weighted mean distance to the centroid of the global species pool (i.e. center of the functional space)
• fmpd (functional mean pairwise distance): The mean weighted distance between all pairs of species
• fnnd (functional mean nearest neighbour distance): The weighted distance to the nearest neighbour within the assemblage

# Matrix of trait values for each morph, i.e. centers of morphs in mspace
# - rows = morphs
# - columns = traits

mo_coord <- as_tibble(morphs$centers) %>%
  mutate(
    morph = row_number(),
    morph = str_pad(morph, width = nchar(n_clust), pad = "0"),
    morph = paste0("morph_", morph)
    ) %>%
  column_to_rownames("morph") %>%
  as.matrix()

# Matrix summarising morphs assemblages
# - rows = profiles (as row names)
# - columns = morphs

weights <- o %>%
  # concentration per date per morph
  group_by(profile_id, morph) %>%
  summarise(n = n()) %>%
  ungroup() %>%
  arrange(morph) %>%
  # convert to wide format and fill with 0s
  pivot_wider(names_from = morph, values_from = n, values_fill = 0) %>%
  column_to_rownames("profile_id") %>% # set profile_id as rowname
  as.matrix()

# Compute diversity metrics, which takes a looooooooong time
morpho_div <- alpha.fd.multidim(
  sp_faxes_coord = mo_coord,
  asb_sp_w = weights,
  ind_vect = c("fdis", "fmpd", "fnnd", "feve", "fric", "fdiv", "fori", "fspe"),
  details_returned = FALSE,
  verbose = FALSE
)

# Clean result
morpho_div <- morpho_div$functional_diversity_indices %>% 
  rownames_to_column(var = "profile_id") %>% 
  as_tibble() %>% 
  select(-sp_richn) %>% 
  # rename metrics from functional to morphological
  set_names(~ str_replace_all(., "^f", "mo_")) 

# And add to table of profiles
profiles <- profiles %>% 
  left_join(morpho_div, by = join_by(profile_id))

Plot maps of resulting morphological diversity metrics

ggmap(profiles, var = "mo_ric", type = "point")

ggmap(profiles, var = "mo_dis", type = "point")

ggmap(profiles, var = "mo_div", type = "point")

ggmap(profiles, var = "mo_eve", type = "point")

ggmap(profiles, var = "mo_ori", type = "point")

ggmap(profiles, var = "mo_spe", type = "point")

ggmap(profiles, var = "mo_mpd", type = "point")

ggmap(profiles, var = "mo_nnd", type = "point")

Explore features

Let’s do a PCA on the features to get the main trends in the dataset.

pl_metrics <- profiles %>% select(prop_crustacea:mo_spe)
pl_pca <- FactoMineR::PCA(pl_metrics, scale.unit = TRUE, graph = FALSE)
plot(pl_pca, choix = "var")

# Get eigenvalues
eig <- pl_pca$eig %>%
  as.data.frame() %>%
  rownames_to_column(var = "comp") %>%
  as_tibble() %>%
  mutate(
    comp = str_remove(comp, "comp "),
    comp = as.numeric(comp),
    comp = as.factor(comp)
    ) %>% 
  rename(var = `percentage of variance`, cum_var = `cumulative percentage of variance`)

eig %>%
  ggplot() +
  geom_col(aes(x = comp, y = eigenvalue)) +
  geom_hline(yintercept = 1, col = "red", linewidth = 0.5) +
  theme_classic() +
  scale_y_continuous(expand = c(0, 0)) +
  labs(x = "PC", y = "Eigenvalue") +
  theme(axis.text.x = element_text(angle = 90, vjust = 0.5, hjust=1))

# Get coordinates of individuals
inds <- pl_pca$ind$coord %>% as_tibble() %>% select(Dim.1:Dim.3)
# Set nice names for columns
colnames(inds) <- str_c("dim_", paste(c(1:ncol(inds))))
df <- profiles %>% 
  select(profile_id, lon, lat, datetime) %>% 
  bind_cols(inds)

ggmap(df, var = "dim_1", type = "point", palette = div_pal)

ggmap(df, var = "dim_2", type = "point", palette = div_pal)

ggmap(df, var = "dim_3", type = "point", palette = div_pal)

df %>% 
  select(lon, lat, contains("dim_")) %>% 
  pivot_longer(contains("dim_")) %>% 
  ggplot(aes(x = lat, y = value)) +
  geom_point(size = 0.5) + 
  geom_smooth() +
  coord_flip() +
  facet_wrap(~name, nrow = 1)

Save

Let’s rename morphospace axes according to what we found to make them more meaningful.

profiles <- profiles %>% 
  rename(
    mo_size_mean = mo_dim1_mean,  # size (positive values = bigger)
    mo_grey_mean = mo_dim2_mean,  # grey (positive values = transparent, i.e. higher grey values)
    mo_elon_mean = mo_dim3_mean,  # elongation (positive values = elongated)
    mo_ghet_mean  = mo_dim4_mean, # grey heterogeneous (positive values = heterogeneous)
    mo_size_sd = mo_dim1_sd,
    mo_grey_sd = mo_dim2_sd,
    mo_elon_sd = mo_dim3_sd,
    mo_ghet_sd  = mo_dim4_sd,
  ) %>% 
  select(-contains("mo_ide"))

#|cache: false
save(profiles, file = "data/01.uvp_profiles.Rdata")